Planckian scattering rate from coherent charge carrier-lattice vibration dynamics

Fermi liquid and Bloch-Grüneisen theories fail to describe strange metal behaviors, e.g. normal state properties of high Tc superconductors. Cuprates, heavy Fermion materials and twisted bilayer graphene exhibit universal linear-in-temperature resistivity which can be obtained by Drude formula with the Planckian scattering rate. Consisting of only Planck and Boltzmann constants, this mysterious scattering rate has eluded explanations. Here we show that a Planckian scattering rate emerges from coherent and non-perturbative interactions of charge carriers and lattice vibrations. Carrier velocities are slowed down due to the strong deformation potential scattering. Two competing mechanisms emerge in this regime: A strong deformation potential tries to localize carriers, but its dynamics (random movement and shape-shifting) induces delocalization. We find that carrier diffusion saturates to the previously conjectured quantum bound of diffusion. We obtain the Planckian scattering rate from the quantum diffusion of carriers and correctly predict the experimentally observed universal linear-in-temperature resistivity for various cuprates.